Let a > 0.

Let x ϵ (0,a) and y ϵ (0,a).

Use the fact that cosh is a primitive of sinh to prove that

|sinh y - sinh x| ≤ (cosh a)|y - x|

Thanks very much for any help.

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- May 26th 2010, 11:11 AMfeyomiProve that |sinh y - sinh x| ≤ (cosh a)|y - x|
Let a > 0.

Let x ϵ (0,a) and y ϵ (0,a).

Use the fact that cosh is a primitive of sinh to prove that

|sinh y - sinh x| ≤ (cosh a)|y - x|

Thanks very much for any help.

- May 26th 2010, 12:30 PMPlato
Use the mean value on $\displaystyle \sinh(t)$ on the interval $\displaystyle [x,y]$.

Note that $\displaystyle \cosh(c)\le \cosh(a)$ if $\displaystyle c<a$.